This paper re-evaluates the relationship between the observed sunward electron cutoff energy and the depth of the Sun's global electrostatic potential. It investigates whether taking into account the effects of local traps formed by magnetic fluctuations provides an alternative explanation for the observed electron deficit. The fluctuations of the highly variable interplanetary magnetic field form a series of shallow magnetic mirror traps that move at approximately the speed of the solar wind. The study investigates the dynamics of electrons as they move outward against an attractive solar electrostatic potential and interact with these traps. By following the motion of the electrons using first-principles calculations, we assess the effect of the traps on the velocity distribution of the particles. Electrons that escape the local trap continue to lose energy as they move outward until they are eventually captured by subsequent traps, preventing them from returning to the observer as sunward-moving particles. We derive a mathematical expression for the cutoff velocity, defined as the limit beyond which particles can no longer overtake the outer endpoint of a local trap. It turns out that the observed cutoff energy characterizes only the local potential drop within a trap, rather than the total depth of the Sun's potential well. The true potential well can be significantly deeper, scaled by the ratio of the radial distance from the Sun to the trap size. Furthermore, electrons captured by these moving traps contribute to the formation of the solar wind core population. The Sun's electrostatic potential is a more significant factor in solar wind acceleration than previously interpreted from cutoff data. The interaction between electrostatic deceleration and moving magnetic traps provides a new framework for understanding the origin and behavior of the solar wind core electrons.
Recent space missions, especially the unprecedented observations of the Parker Solar Probe (Fox et al. 2016), have enabled us to gain previously unattainable knowledge about the nascent solar wind. Based on theoretical considerations, it has long been assumed that the Sun has an electrostatic field (formed because the Sun's gravitational field alone cannot retain the more mobile electrons), which plays a significant role in accelerating solar wind ions (Lemaire & Scherer 1971). Previously, it was not possible to experimentally investigate this field, but recently, some clues pointing to its existence have been discovered in the anisotropies of particle distributions observed near the Sun. Several articles (Berčič et al. 2021;Halekas et al. 2020Halekas et al. , 2021Halekas et al. , 2022;;Raouafi et al. 2023) report that some of the sunward moving electrons are missing above a certain energy level. Since the simplest explanation for the existence of a population moving toward the Sun is that an attractive potential turned back the outmoving particles, the observed energy-dependent cutoff may indicate that above this energy, electrons are able to escape the attractive potential, i.e., the cutoff energy may characterize the depth of the potential relative to the zero potential defined in spatial infinity. Based on the above assumptions, calculating the depth of the potential from the cutoff energy leads to the conclusion that the electric potential of the Sun is significantly lower than what would be necessary to accelerate the solar wind ions to the observed velocities. This conclusion (if true) relegates the electric potential to the role of a minor factor in solar wind accel-⋆ Corresponding author: nemeth.zoltan@wigner.hun-ren.hu eration and reopens the burning question of what process might dominate ion acceleration in the collisionless plasma of the solar wind.
It is tempting to suggest that we should revert to the fluid model of solar wind acceleration pioneered by Eugene Parker (Parker 1958), especially since Nemeth (2025) demonstrated that, under certain conditions, magnetized plasmas can behave as fluids even in the absence of particle-particle collisions. However, simple energy considerations indicate that fluid effects alone cannot fully account for the acceleration of the solar wind. The pressure gradient can only serve to concentrate all the energy distributed among the different degrees of freedom of the particles into a single translational degree of freedom. (This is the same principle, which also underlies the theoretical limit of outflow velocity that can be achieved using a de Laval nozzle.) Simply put, if all particles entering the acceleration region exit on the other side while no additional energy is introduced above the thermal energy already present, then acceleration only means the redistribution of energy between degrees of freedom -hence the upper bound described above. The introduction of an electric potential, particularly one that shifts from attractive to repulsive as an ion moves away from the Sun, addresses this issue (Lemaire 2010;Maksimovic et al. 1997;Zouganelis et al. 2004). Not all particles that enter the process, and contribute energy, will escape the potential well of the Sun. The portion that escapes takes energy away from the remaining plasma, which consequently cools down. This aspect of the acceleration is necessary to allow the observed high speed of the solar wind flow, and this is what is called into question by the new observations.
To resolve this problem, we can proceed in one of two ways: either we try to find a new solar wind acceleration process with appropriate characteristics to replace the electric potential, or we can re-examine the logic that relates the observed cutoff energy of sunward-moving electrons to the depth of the potential well. In this paper, we pursue the second option.
What we can say with certainty based on the observations is that, above a certain energy level, something prevents the outwardmoving electrons from returning to the measurement location. As we saw earlier, one possibility is that these electrons completely leave the potential well and disappear into infinity. The question is whether there is another possibility.
In magnetized plasma, scattering on magnetic fluctuations plays a decisive role in shaping the motion of particles along field lines. These interactions determine not only the parallel pressure (Chew et al. 1956), but also the fundamental nature of plasma behavior (Nemeth 2025). We can thus envision the entire field line system as a complex network of shallow magnetic traps bounded by magnetic fluctuations. If the energy of a particle is sufficiently small, it can be reflected by a strong magnetic fluctuation or can even bounce back and forth in a magnetic bottle formed by two significant field variations.
Add to this the effect of electrons continuously losing energy as they move outward in an attractive poten
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